Last update to our questions: 9/31/16
FAA Private Pilot Question Bank: 09/28/16
We update our questions as often as the FAA updates their questions bank, or as often you report new questions to us.

# Chapter 4 | Small Fixed Wing Aircraft Operational Weight and Balance Computations

Weight and balance data allows the pilot to determine the loaded weight of the aircraft and determine whether or not the loaded CG is within the allowable range for the weight. See Figure 4-1 for an example of the data necessary for these calculations. Figure 4-1. Weight and balance data needed to determine proper loading of a small fixed wing aircraft.

### Determining the Loaded Weight and CG

An important part of preflight planning is to determine that the aircraft is loaded so its weight and CG location are within the allowable limits. [Figure 4-2] There are two ways of doing this: by the computational method using weight, arms, and moments; and by the loading graph method, using weight and moment indexes. #### Computational Method

The computational method uses weights, arms, and moments. It relates the total weight and CG location to a CG limits chart similar to those included in the TCDS and the POH/AFM.

A worksheet such as the one in Figure 4-3 provides space for all of the pertinent weight, CG, and moment along with the arms of the seats, fuel, and baggage areas.

Figure 4-3. Blank weight and balance worksheet.

Figure 4-4. Completed weight and balance worksheet.

When planning the flight, fill in the blanks in the worksheet with the specific data for the flight. [Figure 4-4]

 Pilot .............................................120 lbs Front seat passenger ....................180 lbs Rear seat passenger .....................175 lbs Fuel 88 gal ..................................528 lbs Baggage A ..................................100 lbs Baggage B .....................................50 lbs

Determine the moment of each item by multiplying its weight by its arm. Then determine the total weight and the sum of the moments. Divide the total moment by the total weight to determine the CG in inches from the datum. The total weight is 3,027 pounds and the CG is 43.54 inches aft of the datum.

To determine that the airplane is properly loaded for this flight, use the CG limits envelope in Figure 4-5 (which is typical of those found in the POH/AFM). Draw a line vertically upward from the CG of 43.54 inches, and one horizontally to the right from the loaded weight of 3,027 pounds. These lines cross inside the envelope, which shows the airplane is properly loaded for takeoff, but 77 pounds overweight for landing.

Figure 4-5. Center of gravity limits chart from a typical POH.

Everything possible is done to make flying safe, and one expedient method is the use of charts and graphs from the POH/AFM to simplify and speed up the preflight weight and balance computation. Some use a loading graph and moment indexes rather than the arms and moments. These charts eliminate the need for calculating the moments and thus make computations quicker and easier. [Figure 4-5]

#### Moment Indexes

Moments determined by multiplying the weight of each component by its arm result in large numbers that are awkward to handle and can become a source of mathematical error. To eliminate these large numbers, moment indexes are used. The moment is divided by a reduction factor such as 100 or 1,000 to get the moment index. The loading graph provides the moment index for each component, so you can avoid mathematical calculations. The CG envelope uses moment indexes rather than arms and moments.

CG limits envelope: is the enclosed area on a graph of the airplane loaded weight and the CG location. If lines drawn from the weight and CG cross within this envelope, the airplane is properly loaded.

Figure 4-6 is a typical loading graph taken from the POH of a modern four-place airplane. It is a graph of load weight and load moment indexes. Diagonal lines for each item relate the weight to the moment index without having to use mathematical calculations. #### Compute Weight and Balance Using the Loading Graph

To compute the weight and balance using the loading graph in Figure 4-6, make a loading schedule chart like the one in Figure 4-7.

In Figure 4-6, follow the horizontal line for 300 pounds load weight to the right until it intersects the diagonal line for pilot and front passenger. From this point, drop a line vertically to the load moment index along the bottom to determine the load moment for the front seat occupants. This is 11.1 lb-in/1,000. Record it in the loading schedule chart.

Determine the load moment for the 175 pounds of rear seat occupants along the diagonal for second row passengers or cargo. This is 12.9; record it in the loading schedule chart. Determine the load moment for the fuel and the baggage in areas A and B in the same way and enter them all in the loading schedule chart. The maximum fuel is marked on the diagonal line for fuel in terms of gallons or liters. The maximum is 88 gallons of usable fuel. The total capacity is 92 gallons, but 4 gallons are unusable and have already been included in the empty weight of the aircraft. The weight of 88 gallons of gasoline is 528 pounds and its moment index is 24.6. The 100 pounds of baggage in area A has a moment index of 9.7 and the 50 pounds in area B has an index of 5.8. Enter all of these weights and moment indexes in the loading schedule chart and add all of the weights and moment indexes to determine the totals. Transfer these values to the CG moment envelope in Figure 4-8.

The CG moment envelope is an enclosed area on a graph of the airplane loaded weight and loaded moment. If lines drawn from the weight and loaded moment cross within this envelope, the airplane is properly loaded.

The loading schedule shows that the total weight of the loaded aircraft is 3,027 pounds, and the loaded airplane moment/1,000 is 131.8.

Draw a line vertically upward from 131.8 on the horizontal index at the bottom of the chart, and a horizontal line from 3,027 pounds in the left-hand vertical index. These lines intersect within the dashed area, which shows that the aircraft is loaded properly for takeoff, but it is too heavy for landing.

If the aircraft had to return for landing, it would have to fly long enough to burn off 77 pounds (slightly less than 13 gallons) of fuel to reduce its weight to the amount allowed for landing. Figure 4-8. CG moment envelope.

### Multiengine Airplane Weight and Balance Computations

Weight and balance computations for small multiengine airplanes are similar to those discussed for single-engine airplanes. See Figure 4-9 for an example of weight and balance data for a typical light twin-engine airplane.

Figure 4-9. Typical weight and balance data for a light twin-engine airplane.

The airplane in this example was weighed to determine its basic empty weight and EWCG. The weighing conditions and results are:

 Fuel drained - Oil full - Right wheel scales -1,084 lbs, tare 8 lbs Left wheel scales - 1,148 lbs, tare 8 lbs Nose wheel scales - 1,202 lbs, tare 14 lbs

#### Determine the Loaded CG

Beginning with the basic empty weight and EWCG and using a chart such as the one in Figure 4-11, the loaded weight and CG of the aircraft can be determined. [Figure 4-10]

Figure 4-10. Twin-engine airplane weight and balance diagram.

The aircraft is loaded as shown here:

 Fuel (140 gal) ................... 840 lbs Front seats ........................ 320 lbs Row 2 seats ...................... 310 lbs Fwd. baggage ................... 100 lbs Aft. baggage ....................... 90 lbs

#### Chart Method Using Weight, Arm, and Moments

Make a chart showing the weight, arm, and moments of the airplane and its load.

Figure 4-11. Determining the loaded center of gravity of the airplane in Figure 4-10.

The loaded weight for this flight is 5,064 pounds, and the CG is located at 42.47 inches aft of the datum.

To determine that the weight and CG are within the allowable range, refer to the CG range chart of Figure 4-12. Draw a line vertically upward from 42.47 inches from the datum and one horizontally from 5,064 pounds. These lines cross inside the envelope, showing that the airplane is properly loaded. Figure 4-12. Center of gravity range chart.

#### Determining the CG in Percent of MAC

Refer again to Figures 4-10 and 4-11.

The loaded CG is 42.47 inches aft of the datum.
The MAC is 61.6 inches long.
The LEMAC is located at station 20.1.
The CG is 42.47 - 20.1 = 22.37 inches aft of LEMAC.

Use this formula: The loaded CG is located at 36.3% of the mean aerodynamic chord.

#### The Chart Method Using Weight and Moment Indexes

As mentioned in the previous chapter, anything that can be done to make careful preflight planning easier makes flying safer. Many manufacturers furnish charts in the POH/AFM that use weight and moment indexes rather than weight, arm, and moments. They further help reduce errors by including tables of moment indexes for the various weights.

Consider the loading for this particular flight:

Cruise fuel flow = 16 gallons per hour
Estimated time en route = 2 hours 10 minutes.
Reserve fuel = 45 minutes = 12 gallons
Total required fuel = 47 gallons

The pilot completes a chart like the one in Figure 4-13 using moment indexes from tables in figure 4-14 through 4-16.  The moments/100 in the index column are found in the charts in Figure 4-14 through 4-16. If the exact weight is not in the chart, interpolate between the weights that are included. When a weight is greater than any of those shown in the charts, add the moment indexes for a combination of weights to get that which is desired. For example, to get the moments/100 for the 320 pounds in the front seats, add the moment index for 100 pounds (105) to that for 220 pounds (231). This gives the moment index of 336 for 320 pounds in the front seats.

Use the moment limits vs. weight envelope in Figure 4-17 on page 4-8 to determine if the weight and balance conditions will be within allowable limits for both takeoff and landing at the destination. The Moment limits vs. Weight envelope is an enclosed area on a graph of three parameters. The diagonal line representing the moment/100 crosses the horizontal line representing the weight at the vertical line representing the CG location in inches aft of the datum. When the lines cross inside the envelope, the aircraft is loaded within its weight and CG limits.

Takeoff - 3,781 lbs and 4,310
moment/100

Landing - 3,571 lbs and 4,050
moment/100

Locate the moment/100 diagonal line for 4,310 and follow it down until it crosses the horizontal line for 3,781 pounds. These lines cross inside the envelope at the vertical line for a CG location of 114 inches aft of the datum.

The maximum allowable takeoff weight is 3,900 pounds, and this airplane weighs 3,781 pounds. The CG limits for 3,781 pounds are 109.8 to 117.5. The CG of 114 inches falls within these allowable limits.